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9(3x^2-38x-8)=0
We multiply parentheses
27x^2-342x-72=0
a = 27; b = -342; c = -72;
Δ = b2-4ac
Δ = -3422-4·27·(-72)
Δ = 124740
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{124740}=\sqrt{324*385}=\sqrt{324}*\sqrt{385}=18\sqrt{385}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-342)-18\sqrt{385}}{2*27}=\frac{342-18\sqrt{385}}{54} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-342)+18\sqrt{385}}{2*27}=\frac{342+18\sqrt{385}}{54} $
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